Learn Hardcore Swedish: Hon vill inte ha läxor på lovet, utan bara läsa sina egna böcker. - She does not want homework during the school break, but only to read her own books.

So the comma marks the boundary between the first clause (Hon vill inte ha läxor på lovet) and the contrasting part introduced by utan (bara läsa sina egna böcker).

What exactly does lovet mean? Is it “holiday” or “vacation”?

Lov is specifically a school break (no lessons), like:

sportlov – winter/ski break
sommarlov – summer holiday (from school)
jullov – Christmas holiday (from school)

Lovet (with -et) is the definite form: “the break / the holiday” (that both speaker and listener know about).

It’s different from:

semester – vacation from work (for adults)
helg – weekend or (short) public holiday

So på lovet here is “during the (school) break.”

Why is it läxor and not the singular läxa?

Läxa = one homework assignment.
Läxor = homework in general / multiple assignments.

In practice, läxor (plural) is overwhelmingly more common when talking about “having homework” in general, just like English normally says homework (uncountable), not a homework.

Jag har läxor. – I have homework.
Hon får mycket läxor. – She gets a lot of homework.

Hon vill inte ha läxor sounds natural; hon vill inte ha läxa would suggest one specific assignment and is unusual in this general sense.

Could you also say Hon vill inte ha läxa på lovet?

You could, but it would sound odd or very specific, like:

She doesn’t want to have a homework assignment during the break (one particular task).

For the general idea “no homework on the break,” Swedish strongly prefers the plural läxor:

Hon vill inte ha läxor på lovet. – She doesn’t want homework during the break.

What does på lovet literally mean, and why på and not i or under?

Literally, på lovet is “on the break/holiday”, but idiomatically it means “during the break”.

Swedish often uses på with periods of time, especially repeated or known periods:

på sommaren – in the summer
på vintern – in the winter
på helgen – at / on the weekend
på lovet – during the school break

You can say under lovet (= during the break) and it’s also correct, but på lovet is very natural and common. I lovet would be wrong here.

Why is it sina egna böcker and not hennes egna böcker?

Swedish has a special reflexive possessive for third person: sin / sitt / sina. It refers back to the subject of the same clause.

Hon vill … läsa sina egna böcker.
- sina refers back to hon (the subject): her (own) books.

Hennes also means her, but it does not point back to the subject; it is used when the owner is someone else or when you’re not tying it to the subject grammatically.

Examples:

Hon läser sina böcker. – She is reading her (own) books.
Hon läser hennes böcker. – She is reading her books where her = some other woman.

So in this sentence, because it’s her own books, we must use sina, not hennes.

Why is it sina and not sin or sitt?

Sin / sitt / sina must agree with the noun they refer to:

sin
- en-word singular
  - sin bok – her book
sitt
- ett-word singular
  - sitt hus – her house
sina
- any plural noun
  - sina böcker – her books

Since böcker is plural, the correct form is sina:
sina böcker = her books (referring back to the subject).

What does egna add here? Is it necessary?

Egna means “own”. It adds emphasis that the books belong to her personally, as opposed to borrowed books or school books.

läsa sina böcker – read her books
läsa sina egna böcker – read her own books (extra emphasis)

It is not grammatically necessary. You could say:

Hon vill inte ha läxor på lovet, utan bara läsa sina böcker.

That would still be correct and natural, just slightly less emphatic about ownership.

Why is there no att before läsa?

Two things are happening:

With modal-like verbs such as vill, Swedish often omits att before the infinitive:
- Hon vill läsa. (not vill att läsa)
- Hon kan läsa.
- Hon ska läsa.
In the second part, Swedish leaves out the repeated verb (vill) because it’s understood:
- Full form would be:
  Hon vill inte ha läxor på lovet, utan vill bara läsa sina egna böcker.
- In normal speech/writing, vill is dropped in the second half: … utan bara läsa sina egna böcker.

So you don’t need att here, and you don’t need to repeat vill.

Why is it bara läsa and not läsa bara?

Bara (= only / just) usually comes right before what it limits, often a verb phrase:

Hon vill bara läsa. – She only wants to read.
Hon äter bara frukt. – She only eats fruit.

Läsa bara would sound wrong here; it would suggest emphasis in an unnatural way and is not the usual position for bara.

So:

utan bara läsa sina egna böcker = but only read her own books (natural word order).

Does läsa here mean “read” or “study”?

Läsa can mean both:

To read (books, texts)
- Jag läser en bok. – I am reading a book.
To study (a subject, at a place)
- Jag läser svenska. – I study Swedish.
- Hon läser på universitetet. – She studies at the university.

In this sentence, because it says läsa sina egna böcker, it clearly has the concrete sense “to read her own books”. Any “studying” sense would be secondary here.

What is the difference between ha läxor and göra läxor?

ha läxor = have homework (be assigned homework)
- Jag har läxor. – I have homework.
- Hon vill inte ha läxor på lovet. – She doesn’t want to have homework during the break.
göra läxor = do homework
- Jag måste göra läxor. – I have to do homework.
- Hon vill inte göra läxor på lovet. – She doesn’t want to do homework during the break.

In your sentence, ha läxor focuses on being given homework at all; if you say göra läxor, you emphasise the activity of doing the assignments. Both are grammatically fine, but they highlight different aspects.